Eudoxus of Cnidus

Eudoxus of Cnidus (NY duhs or kuh NY duhs) (400 B.C.?-350 B.C.?) was a Greek astronomer who made important contributions to the field of geometry. He is thought to have contributed to the theory of proportion that can be applied to irrational numbers, and he influenced astronomy with his theories on planetary motion.

Eudoxus was born sometime around 400 B.C., in Cnidus, in southwest Asia Minor, which is now Turkey. His father was Aeschines. At an early age, Eudoxus was influenced by a well-to-do physician, who paid for him to study in Athens. While there, Eudoxus studied geometry. His instructor, Archytas of Tarentum, likely stimulated the young man's interest in number theory and music. Eudoxus also studied medicine and attended lectures by Plato, the Greek philosopher. Eudoxus then traveled to Egypt, where he studied astronomy. He soon became a teacher and founded his own school in Cyzicus, in northwestern Asia Minor. In 368 B.C., he once again visited Athens, this time accompanied by some of his pupils. This move engendered a closer association with Plato, but it is not clear what the relationship was - between Plato's Academy and Eudoxus's school.

Eudoxus made important contributions to both geometry and astronomy. During his lifetime, a problem developed when mathematicians discovered that certain geometric lengths could be expressed only in irrational numbers, or numbers that cannot be expressed as a ratio of two whole numbers. They realized that Pythagorean ideas were incomplete. Around 370 B.C., Eudoxus developed a theory of proportion that resolved problems associated with irrational numbers. From this theory, he also formulated the method of exhaustion, a way of determining areas of curved figures. This theory foreshadowed integral calculus. Also around 370 B.C., Eudoxus worked out a system to explain the motions of the planets. He taught that the planets, the sun and moon, and the stars revolved around the earth. During the 300's B.C., the philosopher Aristotle accepted and added to this earth-centered geometric model.

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